No. Would not work. The bottom of one tub is the top of the next. How do you mount the UTH in the first place? Also, think about what happens to the tub below when you slide one of them open.
If these were good, cheap, options, people would be using them. There's a reason you don't see them in use.
EDIT: About the plastic melting, would you be worried about taking the rack outside when it's 92° there? Perspective...